Let S be the intersection of the solid cylinders x2 + 22

Let S be the intersection of the solid cylinders x2 + z2 1 and Y2 + z2 1. (a) What are the intervals R C R2 and [c, d] C R such that S C R x [c, d]? Which axes correspond to R and which axis corresponds to [c, d]? (b) Find a formula for v(St) (the area of the cross section) for each value of t. (c) Use Cavalieri's principle to calculate the the volume of the torus, v (S). [Hint: The final answer should be v(S) 16 .